Klarinet Archive - Posting 000130.txt from 2010/08

From: "Peter Gentry" <peter.gentry@-----.uk>
Subj: Re: [kl] About clarinet acoustics
Date: Sun, 15 Aug 2010 07:50:40 -0400

Thanks Diego. You have won the lucidity prize for understandable concise
replies. Bravo !

-----Original Message-----
From: Diego Casadei [mailto:casadei.diego@-----.com]
Sent: Sunday, August 15, 2010 12:36 PM
To: The Klarinet Mailing List
Subject: Re: [kl] About clarinet acoustics

Again, I'm replying to different people inside a single email. But now
I need to take some rest... and spend time on my real work :-)

Cheers,
Diego

Tony Pay wrote:
>
> I think I see where the 8cm problem is. Diego has made the assumption
that the 'speed of sound' in the clarinet tube is the same as the speed of
sound in open air.
> But we know that that speed can vary according to other parameters

This is indeed interesting. However, the only explicit statments about
the sound speed in air which I've found can be summarized this way:
1) the temperature is the most important parameter
2) in air, the humidity plays some minor role
3) no dependence on pressure (obviously: the sound waves are the
perturbations of the pressure and they do not depend on the average
value, unless the density is also affected)

I made my measurement without warmup, to be sure that the temperature
was the same as for the room, which I was able to measure within 0.1 C.
Humidity inside the clarinet is by necessity higher, but it should be
really a very small correction, which compared to the precision of my
measurement is completely negligible.

(Needless to say, I did not insert anything inside my clarinet during
the test.)

Jennifer Jones wrote:
>
>> On section 6.1 the plane acoustic waves in air are treated and it is
>> shown that the variations in pressure and particle velocity are in
>> phase. Plane waves are a good approximation for any real acoustic wave
>> in a homogeneous medium far away from the source (more precisely, at
>> distances of many wavelengths or greater). However, this approximation
>> is not valid inside a clarinet.
>
> This seems odd to me. The reed is vibrating and driving vibrations of
> the air column within the clarinet. So I would think that the
> vibrations within the clarinet would be like a section of a spherical
> wave and essentially behave like a planar wave. Why is this not a
> valid approximation?

Section is 6.1 is about parallel waves in an infinite medium. This
means that all fronts are parallel planes orthogonal to the direction of
propagation and that there are no edge effects because the boundaries
are at infinity. Quite significantly different from the inner bore of a
clarinet, I would say.

Note that inside a cavity there are many more possible modes than
parallel waves (which anyway are still there). The include rotation
modes in addition to purely oscillatory modes. Depending on the
frequency and the cavity parameters, only a few modes can propagate for
decent distances: the other are local effects which are dumped in a
short distance.

I don't know the exact details, but my guess that the situation is
different from plane waves in an open space should not be completely
wrong :-)

> I am thinking of antinodes as locations of relative high pressure
> (force per unit area and number of air molecules per unit volume)
> within the clarinet. I am thinking of nodes as locations of low
> pressure (equal to atmospheric pressure).

Please make sure you think in terms of fluctuations dP sperimposed to an
average pressure P. Acoustics in air is all about the evolution of the
dP term. Unfortunately, people simply omit to write dP+P everywhere and
simplifies the notation with dP -> P (which may be difficult to
interpret correctly) when writing equations. Even more confusingly, the
often obtain expressions containing P and implicitly assume that such
symbol means "the root-mean-square measurement of the fluctuation dP on
top of the average pressure value P". Quite easy to get lost!

> What is meant by maximal pressure variations?

The amplitude of the variations of dP is locally maximal in that position.

> (...) since several sources
> indicate that the reed is a point of maximal variation in pressure, my
> impression is that there must be some variation in the central
> tendency (overall pressure).

The reed is the generator of the sound, which is the source from which
all the power of the wave comes from. For this reason, it must
correspond to the absolute maximum of the amplitude. Again, we are
speaking about the amplitude of the small variations dP superimposed
with the constant pressure field P, which is the same everywhere (the
clarinet is open).

> When it is says that there is an antinode at the reed, it seems that
> there should be a high pressure point there (because of the
> displacement of the node 8 cm away from there, into the barrel as
> Diego pointed out). Is this pressure linked to the pitch played?

The reed is _not_ a point of high pressure. The pressure is the same as
in the room. The oscillating reed is the source of the _perturbations_
of the pressure. It is the amplitude of such perturbations which is
maximum.

> Perhaps the pressure is highest when 8 cm corresponds to 1/4
> wavelength of the note being played.

If you were speaking about a generic point, I would also guess so. But
you are speaking about the source hence I guess that the pressure
_variations_ do not depend on the frequency. Well, at least not very
directly. Indeed the player has a different feeling for different
notes, hence she needs to adapt to the response of the instrument.
Assuming that the player can provide the same power for two different
purely sinusoidal waves, than their amplitudes must be equal. But of
course a real sound is the superposition of many waves, each with its
own amplitude, hence I don't know the answer :-)

> I'll try to figure out what note the 8 cm would serve as a quarter
> wavelength for. The first conclusion I come to is that it is the note
> played by the mouthpiece alone.

Not at all. You need at least to add the barrel, because it depends
also on the pipe. But it could be that the barrel is not long enough
for this exercise. Please try

> why we open the right hand pinky d'#/G# key for the
> altissimo notes?

The mechanism is similar to what happens when opening the register hole.
You put a constraint on the modes which can resonate in the
instrument. Opening the correct hole destroys the correct lower
harmonics, so that only the higher ones can survive. What you play is
the lowest possible harmonic compatible with all perturbations induced
by the open holes.

> That there is a high pressure point at the reed is a bit
> counterintuitive to me

More than counterintuitive: it's wrong. Tha maximum refers to the
amplitude of the small perturbations dP of the pressure.

> because when we blow into the clarinet, we are
> expressing high pressure air from inside our mouths into the tube of
> the clarinet.

Yes and no. What we feel is a constant pressure, i.e. a constant
resistance from the tube. But this is because we can't follow the
oscillations. What really happens is that we create an overpressure
when the reed is open. The sequence of pressure "bursts" is the source
of the sound

> I do not understand impedance.

Me neither :-P

> From what I learned in the past,
> impedance is resistance for alternating current. I see that acoustic
> impedance is sound pressure divided by (particle velocity times
> surface area) or acoustic pressure over acoustic volume flow (1, 2).
> It is a measure of resistance to transmission of sound. I see that it
> dampens the frequency of the oscillations. It determines which
> note(s) can be played with a given fingering (3).

There is a close parallelism between acoustics and circuits. As for the
oscillating circuits, you need to work on the complex plane and use the
complex quantity "impedance", whose real part is the resistance which
everybody knows. But there is also the immaginary part there... I'll
let other people to proceed along this route and comment on the rest of
your message :-)

Peter Gentry wrote:
>
> One aspect not discussed here so far is the frequency response of the
reed.
> We all know that hardness and therefore stiffness affects the quality of
the
> sound (from squeaks to buzzes) but not much the intonation.

Correct. The reed has also its own permitted spectrum of oscillations
and cannot do miracles. Likely, good reeds allow us to get a
satisfactory timber out of the instrument, which means that we can get
the desired distribution of power across all harmonics emitted by the reed.

> Does this mean
> that the reed is simply a means of injecting energy via pressure
> fluctuations into the body of the instrument.

Yes. But it act as a valve: the player is actually the source of the power.

> The dynamic result depending
> on the shape of the cylinder and its venting.

No. Dynamics is about the total power of the sound. Being related to
the power, it is related to the source. [Of course there is an
interplay between the vibrating reed and the rest of the instrument (as
with the player).]

> But it must also influence the character of the vibrations in order to
> perceptibly change the timbre.

Yes. As said above, it will be able to excite only a subset of the
modes which are allowed by the acoustic properties of the pipe. A reed
made with a different material would sound different. For example, it
could sound more "metallic" or "brilliant" if it can oscillate at higher
frequencies.

--

Diego Casadei
__________________________________________________________
Physics Department, CERN
New York University bld. 32, S-A19
4 Washington Place 1211 Geneve 23
New York, NY 10003 Mailbox J28310
USA Switzerland
office: +1-212-998-7675 office: +41-22-767-6809
mobile: +39-347-1460488 mobile: +41-76-213-5376
http://cern.ch/casadei/ Diego.Casadei@-----.ch
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